Abstract : The Kolmogorov-Smirnov test is compared to the median for one-sided and two-sided alternatives. In the two-sided case, although the asymptotic Bayes risk efficiency is the same for symmetric unimodal distributions, the relative efficiency approaches one slowly. In the one-sided case, the efficiency depends heavily on the test. For uniform alternatives, the K-S test is much better than the median, and the test based on the difference of the positive and negative deviations is still better. This latter test appears to have good properties even when the one-sided K-S test does not. (Author)